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IJAMR International Journal of Applied Mathematical Research E-ISSN 2227-4324

Projective synchronization of chaotic systems via backstepping design

Authors and Affiliations

  • Anindita Tarai Aligunj R.R.B High School
  • Mohammad Ali Khan

About this article

DOI
https://doi.org/10.14419/ijamr.v1i4.240
Received
12-07-2012
Accepted
08-08-2012
Published
04-09-2012
Views
1159
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841
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Abstract

Chaos synchronization of discrete dynamical systems are investigated. An algorithm is proposed for projective synchronization of chaotic 2D Duffing map and chaotic Tinkerbell map. The control law was derived from the Lyapunov stability theory. The numerical simulation results are presented to verify the effectiveness of the proposed algorithm.

References

[1] L.M. Pecora and T.L. Carroll , Synchronization in chaotic systems, Phys. Rev. Lett, 64 (1990) 821-824.

[2] S.Hayes, C.Grebogi and E.Ott, Communicating with chaos, Phys. Rev. Lett. 70(1993) 3031-3034.

[3] B. Blasius, A.Huppert, L.Stone, Complex dynamics and phase synchronization in spatially extended ecological systems, Nature, 399 (1999) 354-359.

[4] U. Parlitz, L.Junge and L.Kocarev, Synchronization-based parameter estimation from time series, Phys. Rev. E, 54 (1996) 6253-6259.

[5] M. Rosenblum, A.Pikovosky and J.Kurths, Phase synchronization of chaotic oscillators, Phys. Rev. Lett,76 (1996) 1804-1807.

View more references (13)

[6] N. F. Rulkov, M.M.Suschik and L.S.Tsimring, Generalized synchronization of chaos in directionally coupled chaotic systems, Phys. Rev.E. 51 (1995) 980-994.

[7] S. Poria, The linear generalized chaos synchronization and predictability, Int.J.of Applied Mechanics and Engineering, 12(2007) 879-885.

[8] M. A. Khan and A.K.Mandal, Generalized chaos synchronization of coupled Rossler systems, Bull.Cal.Math.Soc, 101(2009) 197-204.

[9] M. A. Khan, S.N.Pal and S.Poria, Generalized anti-synchronization of different chaotic systems, Int. J. of Applied Mechanics and Engineering, 17(2012) 83-89.

[10] A. Tarai(Poria), S. Poria and P. Chatterjee, Synchronization of bidirectionally coupled chaotic Chen's system with delay, Chaos Solitons and Fractals, 41 (2009) 643-647.

[11] A. Tarai, S.Poria and P. Chatterjee, Synchronization of generalized linearly bidirectionally coupled unified system, Chaos Solitons and Fractals. 40 (2009) 885-892.

[12] M. A. Khan, A. K. Mondal and S. Poria, Three control strategies for unified chaotic system, Int. J. of Applied Mechanics and Engineering, 16 (2011) 597-608.

[13] Yongguang Y, Suochun Z., Controlling uncertain Lu system using backstepping design, Chaos, Solitons & Fractals, 15 (2003) 897-902.

[14] C.Wang and S.S. Ge, Adaptive synchronization of uncertain chaotic systems via backstepping design, Chaos,Solitons & Fractals,12 (2001) 1199-1206.

[15] X.Tan, J.Zhang and Y.Yang, Synchronizing chaotic systems using backstepping design, Chaos, Solitons & Fractals 16 (2003) 37-45.

[16] J. A. Laoye, U. E. Vincent and S. O. Kareem, Chaos control of 4D chaotic systems using recursive backstepping nonlinear controller , Chaos,Solitons & Fractals 32(2007) 1823-1829.

[17] J. M. Gonzalez-Miranda, Amplification and displacement of chaotic attractors by means of unidirectional chaotic driving, Phys. Rev. E, 57(1998) 7321-7324.

[18] R. Mainieri and J. Rehacek, Projective synchronization in three-demensional chaotic system, Phys. Rev. Lett., 82 (1999) 3042-3045.


How to Cite

Tarai, A., & Khan, M. A. (2012). Projective synchronization of chaotic systems via backstepping design. International Journal of Applied Mathematical Research, 1(4), 531-540. https://doi.org/10.14419/ijamr.v1i4.240

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